Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T21:13:45.218Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag on a sphere in unsteady motion in a liquid at rest

Published online by Cambridge University Press:  12 April 2006

S. K. Karanfilian  and
T. J. Kotas
S. K. Karanfilian
Affiliation:
Department of Mechanical Engineering, Queen Mary College, Mile End Road, London E1 4NS
T. J. Kotas
Affiliation:
Department of Mechanical Engineering, Queen Mary College, Mile End Road, London E1 4NS
Get access Rights & Permissions [Opens in a new window]

Abstract

A sphere was subjected to a simple harmonic motion in an otherwise undisturbed liquid. Records of the resistance of the liquid to the motion for various amplitudes and frequencies were obtained. The resistance was first represented by an equation consisting of three terms with empirical coefficients: the steady-motion drag, a term due to the ‘added mass’ and a term due to the history of the motion. It was found that the data could be correlated only with a large degree of scatter by this type of equation. Subsequently an attempt was made to represent the resistance by means of a single term, with an empirical coefficient C. It was found that C correlated well with the acceleration number Vd/V2 and the Reynolds number Vd/v, where V, V and d are the acceleration, velocity and diameter of the sphere respectively and v is the kinematic viscosity of the liquid. C increased with Vd/V2 and decreased in the limit to the steady-motion drag coefficient Cd when Vd/V2 became very small. The range of the Reynolds number in the experiments was 102 < Vd/v < 104 and the range of the acceleration number was 0 ≤ Vd/V2 ≤ 10·5.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 1 , 12 July 1978 , pp. 85 - 96
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209–221.Google Scholar
Baird, M. H. I., Senior, M. G. & Thompson, R. J. 1967 Terminal velocities of spherical particles in a vertically oscillating liquid. Chem. Engng Sci. 22, 551–558.Google Scholar
Basset, A. B. 1888 On the motion of a sphere in a viscous liquid. Phil. Trans. Roy. Soc. A 179, 43–63.Google Scholar
Batailler, G. 1956 Sur la similitude des champs de vitesses et des sillages courts en régimes accélérés. C.R. Acad. Sci. Paris 242, 2619–2621.Google Scholar
Boussinesq, J. 1885 Sur la résistance qu'oppose un liquide⃛au mouvement varié d'une sphere solide⃛et produits soient négligeables. C.R. Acad. Sci. Paris 100, 935–937.Google Scholar
Bugliarello, G. 1956 La resistenza al moto accelerato di sfere in acqua. Ricerca Scientifica 26, 437–461.Google Scholar
Carstens, M. R. 1952 Accelerated motion of spherical particles. Trans. Am. Geophys. Un. 33, 713–721.Google Scholar
Davies, C. N. 1945 Definitive equations for the fluid resistance of spheres. Proc. Phys. Soc. 57, 259–270.Google Scholar
Dubuat, P. L. G. 1786 Principes d'Hydraulique, 2nd edn, vol. 2, pp. 226–259, Paris: De L'imprimerie de Monsieur.
Hamilton, W. S. & Lindell, J. E. 1971 Fluid force analysis and accelerating sphere tests. Proc. A.S.C.E. 97 (HY6), 805–817.Google Scholar
Houghton, C. 1963 The behaviour of particles in a sinusoidal velocity field. Proc. Roy. Soc. A 272, 33–43.Google Scholar
Iversen, H. W. & Balent, R. 1951 A correlating modulus for fluid resistance in accelerated motion. J. Appl. Phys. 22, 324–328.Google Scholar
Keim, S. R. 1956 Fluid resistance to accelerated cylinders. Proc. A.S.C.E. 82 (HY6), 1–14.Google Scholar
Krishnaiyar, N. C. 1923 An experimental determination of the inertia of a sphere vibrating in a liquid. Phil. Mag. Ser. 6, 46, 1049–1053.Google Scholar
Lapple, C. E. & Shepherd, C. B. 1940 Calculation of particle trajectories. Indus. Engng Chem. 32, 605–617.Google Scholar
Lighthill, M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. Roy. Soc. A 224, 1–23.Google Scholar
Luneau, J. 1948 Sur l'effet d'inertie des sillages de corps se déplaceant dans un fluide d'un mouvement uniformément accéléré. C.R. Acad. Sci. Paris 227, 823–825.Google Scholar
Lunnon, R. G. 1926 Fluid resistance to moving spheres. Proc. Roy. Soc. A 110, 302–326.Google Scholar
Mcnown, J. S. & Keulegan, G. H. 1959 Vortex formation and resistance in periodic motion. Proc. A.S.C.E. 85 (EM1), 1–6.Google Scholar
Mcnown, J. S. & Newlin, J. J. 1951 Drag of spheres within cylindrical boundaries. Proc. 1st U.S. Nat. Cong. Appl. Mech. pp. 801–806.
Odar, F. & Hamilton, W. S. 1964 Forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302–314.Google Scholar
Poisson, S. D. 1832 Sur les mouvements simultanés d'un pendule et de l'air environnant. Mém. Acad. Sci. Paris 11, 521–582.Google Scholar
Sarpkaya, T. 1975 Forces on cylinders and spheres in a sinusoidally oscillating fluid. J. Appl. Mech., Trans A.S.M.E. E 42, 32–37.Google Scholar
Schiller, L. & Nauman, A. 1933 Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Z. Ver. dsche. Ing. 77, 318–320.Google Scholar
Schöneborn, P.-R. 1975 Bewegung einzelner Partikeln im instationären Strömungsfeld. Chem. Ing. Tech. 47, 305.Google Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106.Google Scholar